Well, things are wrong if we shouldn't do them; they're right if we should. As for which specific things, there are many. Some people think they can boil it down to a simple principle or two (e.g. things are right if they produce the largest balance of good consequences over bad.) Other people think right and wrong are too varied for anything more than rules of thumb.
Who can say what's right and what's wrong? If you mean who's qualified to pass judgment, then pretty much all of us are—at least about some things. It's wrong to mock people's infirmities. It's wrong to beat someone up because you're annoyed by something he said. It's wrong to kill someone so that you can collect on her insurance policy. And so on. You're in just as good a position as I am to make those claims.
(Of course if you're asking who can make something right or wrong by declaring it right or wrong, there's a pretty good case that no one can. What's right and wrong isn't up to us.)
Does it make a difference to know the...

It's a fascinating question. When the recruit "sees the elephant," as you put it, they seem to gain something that calls out for an epistemological characterization, but just what they gain is harder to say. The problem is that the obvious suggestions don't seem to work. The recruit already that s/he is mortal. Likewise, his or her probabilities haven't shifted. The recruit presumably already thought that death is certain.
So what might the recruit have gained if not knowledge or improved probability judgments? One answer is salience. It's one thing to know something; it's another for it to figure significantly in your outlook. If something is salient for me, it plays a different role in guiding my actions than it does for someone who knows it's true but gives it little thought.
On one model, our actions are guided by probabilities and judgments of importance or value/disvalue. But not everything that we know or believe plays a role in our decision-making, and likewise not everything we see as good or...

An incomplete answer, but relevant, I hope.
Suppose the question is: did Prof. Geisler show up for class on Monday? We ask students enrolled in the class. All the students who were there in the room at class time say yes: Prof. Geisler was there. In fact, she arrived on time, and taught a full class.
Let's grant that every person in the room had a slightly different take on exactly what went on in the room at that time. Let's also grant that some of what some people would say happened will be inaccurate, and may reflect their biases and psychological idiosyncrasies. The question, however, is whether Prof. Geisler showed up. There's no reason to think these differences in perception got in the way of judging that .
In one way this is a trivial example, but it reflects something extremely common. Even with our very real quirks and biases, there's an enormous amount of what we perceive and believe for which those quirks and biases are simply irrelevant. Individually, most of these facts may be...

I think the best answer is that there's no one answer.
Let's start with the easiest of your questions: you've read a biography of someone you've never met. Do you know them? Most people would say "No" because when we say things like "I know Robin," we generally mean that we are acquainted with Robin--have actually met Robin. Knowing about someone is knowledge by description but not by acquaintance, to borrow Bertrand Russell's terms.
In the other cases, there's no simple answer because the terms "mere acquaintance," "friend," "close friend" and so on aren't precise; there's no cut-off. It's like the case of baldness. There's no exact point at which a formerly hirsute person becomes unequivocally bald.* The case you've focused on is an instance of a very general phenomenon. Some people are definitely tall, some are not tall, and some are on the border. Some bananas are definitely ripe, some are not, and for some there's no definite right answer. As you can see, it would be easy to make a very...

As it turns out, we don't get paid. One reason is that, as you may have noticed, there's no charge to ask a question and there's no tip jar. ;-)
On to the question. It's an empirical question; it depends on how our minds and bodies actually work. But it's pretty safe to say that the answer is yes: sometimes you can tell things about a person by the look in their eyes. It's far from perfect and not always reliable, but there's no completely reliable way to know what a person's state of mind is, so that's not a special problem for this case.
In fact, there's not much mystery here from the point of view of common sense. Most of us are at least tolerably good at reading facial expressions. And as for the eyes, they're part of the expression. A fake smile won't give you crow's feet; a genuine smile raises the cheeks and makes the corners of the eyes crinkle. We can learn to tell the difference. That's just one example.
Of course, it's not always so simple. A person's facial expression (eyes especially) may...

I guess I'd have to disagree with the idea that "all of philosophy and logic point to a reason or cause for everything." There's certainly no argument from logic as such; it's perfectly consistent to say that some events are genuinely random. Some philosophers have held that there's a reason (not necessarily a cause in the physical sense, BTW) for everything, but the arguments are not very good.
On the other hand... quantum mechanics is a remarkably well-confirmed physical theory that, at least as standardly interpreted, gives us excellent reason to think that some things happen one way rather than another with no reason or cause for which way they turned out.
An example: suppose we send a photon (a quantum of light) through a polarizing filter pointed in the vertical direction. We let the photon travel to a second polarizing filter, oriented at 45 degrees to the vertical. Quantum theory as usually understood says that there's a 50% chance that the photon will pass this filter and a 50% chance that it...

There are two questions here: first, can Descartes' cogito be doubted—is it open to doubt that "I" exist? Second, more generally, is there anything that's not open to legitimate or reasonable or rational doubt? (What people are psychologically capable of doubting maybe another matter.)
On the first, may philosophers would say yes. Even if it's certain that there's thinking going on, it doesn't follow that there's some one or some thing doing the thinking. Consider the Buddhist/ Humean "no self" view. On that way of understanding things, there's no substantial self. There is, as the Humean might say, just a bundle of perceptions. "I think," on this account, is just a manner of speaking. We can't get from "there is thinking" to "I exist."
So maybe it's open to doubt that I exist. Is it open to doubt that there's thinking going on when it seems that there is? Maybe not, though I don't doubt that some clever philosopher could offer an interesting argument to the contrary. What else? Can it...

It's a good question and the answer seems pretty plausibly to be yes. The impression that people have of themselves can often be off the mark, and that can be shown by how they actually behave. Someone who thinks he's generous might really be stingy, always finding excuses not to contribute his fair share. Someone who thinks she's not very smart might actually have a lot of insight, as those who know her can plainly see. And on it goes. We're complicated beings. There's no reason a priori to think that the part of our minds that tries to make sense of ourselves overall is likely to be especially good at it. No doubt there are some things about ourselves that we're in a better position than others to know, but when it comes to the larger patterns and dispositions that go into making us who we are, disinterested outsiders may well be in a better position than we are to get things right.

I think the simplest answer is this: empiricists think beliefs about matters of fact should be grounded in empirical evidence; they don't think the evidence always has to be direct. I've never been to New Zealand, but I have a considerable amount of indirect empirical evidence that it exists. To take just one bit of that evidence: people whom I know to be otherwise reliable and honest tell me they've been there. On the other hand, I don't even have indirect evidence that Middle Earth exists. What I have is evidence for is that J. R. R. Tolkien wrote stories about a fictional place called Middle Earth, which neither he nor anyone else claimed was real. The (small) larger point is this: the one-word name of a view is not always the best way to figure out what the view actually comes to. Very few, if any, self-described empiricists have said that evidence always has to be direct to be relevant.